Search results for "CONSTANT"

Aggregation and sedimentation of active Brownian particles at constant affinity.

2019

We study the motility-induced phase separation of active particles driven through the interconversion of two chemical species controlled by ideal reservoirs (chemiostats). As a consequence, the propulsion speed is non-constant and depends on the actual inter-particle forces, enhancing the positive feedback between increased density and reduced motility that is responsible for the observed inhomogeneous density. For hard discs, we find that this effect is negligible and that the phase separation is controlled by the average propulsion speed. For soft particles and large propulsion speeds, however, we predict an observable impact on the collective behavior. We briefly comment on the reentrant…

The goldfish--a colour-constant animal.

1996

A series of either thirteen or fifteen coloured test fields with hues from blue through grey to yellow were presented on a black background. Goldfish were trained on a bluish-grey test field by food reward. In the training situation, the setup with the coloured papers was illuminated with white light. In the test situation, the colour of the illumination was changed to blue or yellow. In both test illuminations the goldfish preferred the training field in the same way as under white illumination despite the fact that this test field stimulated the cone types very differently from the training situation. As test fields were present that excited the cones in exactly the same way as under whi…

Nonlocal Cheeger and Calibrable Sets

2019

Given a non-null, measurable and bounded set \(\Omega \subset \mathbb {R}^N\), we define its J-Cheeger constant

Improved Constructions of Quantum Automata

2008

We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use $\frac{4}{\epsilon} \log 2p + O(1)$ states to recognize a language that requires p states classically. The construction is both substantially simpler and achieves a better constant in the front of logp than the previously known construction of [2]. Similarly to [2], our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some preliminary results in this direction.

The constant osculating rank of the Wilking manifold

2008

We prove that the osculating rank of the Wilking manifold V3 = (SO (3) × SU (3)) / U• (2), endowed with the metric over(g, )1, equals 2. The knowledge of the osculating rank allows us to solve the differential equation of the Jacobi vector fields. These results can be applied to determine the area and the volume of geodesic spheres and balls. To cite this article: E. Macias-Virgos et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2007 Academie des sciences.

The Ptolemy and Zbăganu constants of normed spaces

2010

Abstract In every inner product space H the Ptolemy inequality holds: the product of the diagonals of a quadrilateral is less than or equal to the sum of the products of the opposite sides. In other words, ‖ x − y ‖ ‖ z − w ‖ ≤ ‖ x − z ‖ ‖ y − w ‖ + ‖ z − y ‖ ‖ x − w ‖ for any points w , x , y , z in H . It is known that for each normed space ( X , ‖ ⋅ ‖ ) , there exists a constant C such that for any w , x , y , z ∈ X , we have ‖ x − y ‖ ‖ z − w ‖ ≤ C ( ‖ x − z ‖ ‖ y − w ‖ + ‖ z − y ‖ ‖ x − w ‖ ) . The smallest such C is called the Ptolemy constant of X and is denoted by C P ( X ) . We study the relationships between this constant and the geometry of the space X , and hence with metric fix…

Cotype 2 estimates for spaces of polynomials on sequence spaces

2002

We give asymptotically correct estimations for the cotype 2 constant C2(P(mXn)) ofthe spaceP(mXn) of allm-homogenous polynomials onXn, the span of the firstn sequencesek=(\gdkj)j in a Banach sequence spaceX. Applications to Minkowski, Orlicz and Lorentz sequence spaces are given.

On the lattice of J-subnormal subgroups

1992

Lengths of radii under conformal maps of the unit disc

1999

If E f ( R ) E_{f}(R) is the set of endpoints of radii which have length greater than or equal to R > 0 R>0 under a conformal map f f of the unit disc, then cap ⁡ E f ( R ) = O ( R − 1 / 2 ) \operatorname {cap} E_{f}(R)=O(R^{-1/2}) as R → ∞ R\to \infty for the logarithmic capacity of E f ( R ) E_{f}(R) . The exponent − 1 / 2 -1/2 is sharp.

Quantum Algorithm for Dyck Language with Multiple Types of Brackets

2021

We consider the recognition problem of the Dyck Language generalized for multiple types of brackets. We provide an algorithm with quantum query complexity \(O(\sqrt{n}(\log n)^{0.5k})\), where n is the length of input and k is the maximal nesting depth of brackets. Additionally, we show the lower bound for this problem which is \(\varOmega (\sqrt{n}c^{k})\) for some constant c.